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Proceedings Paper

Sandwich distances
Author(s): Jean-Marie Becker; Dinu Coltuc; Michel Jourlin
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Paper Abstract

Many authors, e.g., Rosenfeld and Pfaltz, Borgefors..., have proposed efficient and/or accurate approximations of euclidian distance on a 2D or 3D grid with methods which are connected, more or less directly, to norm derived distances, e.g., with Lp norms. This paper enlarges the scope in a continuous and m-dimensional framework. It presents a new broad class of distances, called 'sandwich' or 'periodic' distances. They are obtained by compounding in a periodic manner a certain number of norm-derived distances. The main result of this paper is the proof of a sufficient condition under which the triangular inequality is fulfilled, i.e., that the unit balls of the compounded distances belong to an ascending chain. Moreover, the theory includes weighted distances, giving this tool a high degree of flexibility.

Paper Details

Date Published: 20 October 1997
PDF: 11 pages
Proc. SPIE 3168, Vision Geometry VI, (20 October 1997); doi: 10.1117/12.279652
Show Author Affiliations
Jean-Marie Becker, Ecole Superieure de Chimie Physique Electronique de Lyon (France)
Dinu Coltuc, Polytechnical Univ. Bucharest (Romania)
Michel Jourlin, Ecole Superieure de Chimie Physique Electronique de Lyon (France)

Published in SPIE Proceedings Vol. 3168:
Vision Geometry VI
Robert A. Melter; Angela Y. Wu; Longin Jan Latecki, Editor(s)

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